"I love all members of our team and sometimes you don't agree with every member of your team but it's a great team and I hope we keep it together," he said.

Labor frontbencher Tony Burke wasn't surprised about the reports.

"We've been watching a split in the coalition for more than a year now and it's going to continue to unravel," he said.

Speculation about Senator Bernardi's defection comes as voter support for One Nation surged in the first Newspoll of the year.

The minor party garnered eight per cent of the national primary vote - double its Senate numbers at the July election - as support for the government tumbled.

Backing for the coalition has dropped to its lowest level since Mr Turnbull toppled Tony Abbott as prime minister in September 2016.

After preferences Labor leads the coalition 54-46 per cent.

Nationals MP George Christensen says Senator Bernardi is a waste of talent on the backbench.

"Cory should be put on the frontbench of the coalition, he's got that much to offer," he told reporters in Canberra.

As to his own future, Mr Christensen insisted he is loyal to Nationals leader Barnaby Joyce and the party.

He hasn't spoken to Senator Bernardi in about a week.

"So I'm here in the government so long as the government holds true to the values of the people that put us there," he said.

The backbencher says the government has to reconnect with disgruntled voters and party members.

"I really do hope that we succeed in doing that because if we drift away any further it's going to become untenable."

Colleagues agitating fresh moves for a free vote on same-sex marriage were been unhelpful and the "show's over" if there was any move to ditch the government's plebiscite policy.

Veteran Liberal senator Eric Abetz says he remains committed to the Liberal Party and its founding principles.

He called on every Liberal member to remain "within the tent" and work together.

But he conceded some conservative MPs had been deliberately sidelined under Mr Turnbull's leadership and that had affected support from the party's base.

"I believe that there has to be more reaching out to the conservatives," he told Sky News on Monday.

Cabinet minister Arthur Sinodinos said the prime minister has been "very concerned" to make sure that all tributaries of the Liberal Party have their say when it came to policy - and has even attracted criticism for doing so.

"The fact is he's weaved his way through in a way which is consistent with trying to be the leader of a broad church," he told ABC radio.

Senator Sinodinos said he didn't know what Senator Bernardi was going to do, but labelled him a "good fellow".

"I like him and like all good Liberals I'd like him to be in the Liberal Party, but I'm not speculating what will happen tomorrow."